Sarah left on the interstate at a speed of 60 mph. Her sister followed her on the same route, leaving 2 hours later at a rate of 65 mph. How long will it take for Sarah's siter to catch up with Sarah?
let the time taken to catch up be t hours
distance covered by the sister be 65t
distance covered by Sarah is 60(t+2)
but the went the same distance, so ...
65t = 60(t+2)
solve for t
24
To find out how long it will take for Sarah's sister to catch up with Sarah, we can set up an equation based on their speeds.
Let's assume the time it takes for Sarah's sister to catch up is "t" hours.
We know that Sarah traveled for 2 hours before her sister started. So, Sarah's travel time will be "t + 2" hours.
Now, let's set up an equation using the formula: Distance = Speed × Time
Distance covered by Sarah = Distance covered by Sarah's sister
60(t + 2) = 65t
Simplifying the equation:
60t + 120 = 65t
Subtracting 60t from both sides:
120 = 5t
Dividing both sides by 5:
t = 24
Therefore, it will take Sarah's sister 24 hours to catch up with Sarah.
To find out how long it will take for Sarah's sister to catch up with Sarah, we can use the concept of relative speed.
Relative speed is the speed at which one object is moving relative to another. In this case, Sarah's sister is trying to catch up to Sarah, so her relative speed is the difference between her speed and Sarah's speed.
Sarah's speed = 60 mph
Sarah's sister's speed = 65 mph
Relative speed = Sarah's sister's speed - Sarah's speed = 65 mph - 60 mph = 5 mph
Now, we can set up a distance equation to solve for the time it takes for Sarah's sister to catch up with Sarah:
Distance = Speed x Time
Since Sarah has a head start, we need to take into account the distance she has already traveled. She left 2 hours earlier and was traveling at a speed of 60 mph, so her distance is:
Distance Sarah = Sarah's speed x Time = 60 mph x 2 hours = 120 miles
Now, let's denote the time it takes for Sarah's sister to catch up as "t" hours. The distance Sarah's sister travels in that time is:
Distance Sarah's sister = 65 mph x t hours
Since Sarah's sister is catching up to Sarah, their distances will be equal when they meet. So we can set up the equation:
Distance Sarah = Distance Sarah's sister
120 miles = 65 mph x t hours
Now we can solve for "t":
t = 120 miles / 65 mph
Using a calculator, we find that t is approximately 1.85 hours. Therefore, it will take Sarah's sister approximately 1.85 hours (or 1 hour and 51 minutes) to catch up with Sarah.